In the remainder of this manuscript we focus our presentation on the single field Poisson problem (REF ), discretized by quasi-uniform meshes with \(C^0\) -continuous piecewise polynomial basis functions of order \(p\) . The presented analyses and methods naturally extend to vector-valued problems that can be expressed as a Cartesian product of scalar fields (i.e., one field per space dimension). Mixed formulations and discretizations with local refinements are not discussed in detail, but, unless otherwise specified, the provided insights also carry over mutatis mutandis to these cases. Curl-conforming and div-conforming problems (i.e., posed in \(H(\text{curl};\Omega )\)  or \(H(\text{div};\Omega )\) , respectively), suffer from similar problems with stability and conditioning on small cut elements as the grad-conforming problems (posed in \(H^1(\Omega )\) ) considered here. With respect to conditioning, maximum continuity splines as commonly used in isogeometric analysis [1]}, [2]} can behave differently from \(C^0\) -continuous bases. Therefore, Section  also considers B-spline bases as a special case.
